Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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FEYNMAN INTEGRALS, DIFFUSION PROCESSES AND QUANTUM SYMPLECTIC TWO-FORMS

  • Published : 2001.03.01
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Abstract

This is an introduction to a stochastic version of E. Cartan′s symplectic mechanics. A class of time-symmetric("Bernstein") diffusion processes is used to deform stochastically the exterior derivative of the Poincare-Cartan one-form on the extended phase space. The resulting symplectic tow-form is shown to contain the (a.e.) dynamical laws of the diffusions. This can be regarded as a geometrization of Feynman′s path integral approach to quantum theory; when Planck′s constant reduce to zero, we recover Cartan′s mechanics. The underlying strategy is the one of "Euclidean Quantum Mechanics".

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